Simplify. \[ \sqrt{24 y^{8}} \] Assume that the variable $y$ represents a positive real number. $\square$ \[ \sqrt{\square} \quad \square \]

Step 1 ：The given expression is \(\sqrt{24 y^{8}}\).

Step 2 ：24 can be factored into 4 and 6, where 4 is a perfect square.

Step 3 ：\(y^{8}\) can be written as \((y^{4})^{2}\), which is also a perfect square.

Step 4 ：So, we can simplify the expression by taking the square root of these perfect squares.

Step 5 ：The simplified expression is \(2\sqrt{6}y^{4}\).

Step 6 ：Final Answer: The simplified form of the given expression is \(\boxed{2\sqrt{6}y^{4}}\).